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Tritet Jr. is equal to $$4 \uparrow\uparrow 4$$ in up-arrow notation[1], or $$\lbrace 4,4,2 \rbrace$$ in BEAF.[2] The number used to be called tritet, a much larger number named and renamed by Jonathan Bowers. Sbiis Saibian coined the new name. Using Alistair Cockburn's megafuga- prefix, Tritet Jr. can be named "megafugafour".[3] It can also be named "boogafour" using the booga- prefix, or "troogatwo" using the trooga- prefix.

It is approximately $$10^{8.0723 \times 10^{153}}$$, meaning that it's somewhat larger than a googolplex. The decimal expansion of Tritet Jr. is: 23,610,226,714,597,313,206............36,860,456,095,261,392,896. The leading digits are computed using logarithms and the terminating digits are computed using modular exponentiation.

Its exact value can be computed using basic laws of algebra: $$4\uparrow\uparrow4 = 4^{4^{4^{4}}} = 4^{4^{256}} = 4^{2^{512}} = 2^{2^{513}}$$.

It is currently unknown, whether its successor, which is the 513th Fermat number, is composite or prime.[4]

Wiki user Hyp cos calls this number a tetbo, and it's equal to s(4,4,2), s(4,2,3), s(4,2,1,2), or s(4,2{2}2) in strong array notation. [5]

-illion name

Using Jonathan Bower's -illions series, some -illion name terms for Tritet Jr. are:

Approximations

Notation Lower bound Upper bound
Down-arrow notation $$4\downarrow\downarrow257$$
Steinhaus-Moser Notation 79[3][3] 80[3][3]
Copy notation 7[7[154]] 8[8[154]]
H* function H(2H(50)) H(3H(50))
Taro's multivariable Ackermann function A(3,A(3,509)) A(3,A(3,510))
Pound-Star Notation #*((1))*(2,8,7,10,3)*11 #*((1))*(9,0,9,2,7,5)*8
Hyper-E notation E[4]1#4
Bashicu matrix system (0)(1)[22] (0)(1)[23]
Hyperfactorial array notation (96!)! (97!)!
Fast-growing hierarchy $$f_2(f_2(504))$$ $$f_2(f_2(505))$$
Hardy hierarchy $$H_{\omega^22}(504)$$ $$H_{\omega^22}(505)$$
Slow-growing hierarchy $$g_{\omega^{\omega^{\omega^\omega}}}(4)$$